Composite observer-based feedback design for singularly perturbed systems via LMI approach

The ε-independent of a class of singularly perturbed systems is consider through the observer-based feedback design for singularly perturbed continuous-time systems. Based on the Lyapunov stability theorem and the tool of linear matrix inequality (LMI), a sufficient condition is derived for the stabilization of singularly perturbed systems. For observer-based feedback design, we first obtain a set of common positive define matrices, observer gain and controller gain of the slow and fast subsystems of the singularly perturbed system via LMI approach. Then the composite observer feedback design will stabilize for the original system. By the ε-bound issue, the proposed stabilization schemes can stabilize the singularly perturbed continuous-time systems for all ε ϵ(0, ε*) and the allowable upper bound ε* can be determined by some algebra approach. A practical example is given to illustrate the validity of the stabilization design.